zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation. (English) Zbl 0872.34033

The aim is to investigate the structure of the homoclinic and heteroclinic solutions of the scalar fourth order equation

γu (4) -βu '' +F ' (u)=0,

with γ,β>0. The two primary examples

F 1 (u)=1 4(u 2 -1) 2 andF 2 (u)=2 π 2 (1+cosπu)

are considered as a background of the theory. The authors construct a countable family of multitransition homoclinic and heteroclinic solutions. The glueing method applied in the paper can also be used to obtain periodic orbits which are in an arbitrarily small neighborhood of the heteroclinic loop and are structurally similar to those which would be found using dynamical methods of Devaney. Also, the existence of the family of homoclinic and heteroclinic solutions described is sufficient to show that the dynamics are chaotic.

34C37Homoclinic and heteroclinic solutions of ODE